Well, considering that your goal is to reach a lot of users, these things are very clear:
- You should setup a site on shared hosting somewhere
- Get a real domain name and point to your site
- On said site you should have a web service to handle the auth, lists etc
I would absolutely not use my home connection, even for a very small number of users. Too much risk for downtime etc, plus unneeded hassle with domain names if/when you decide to grow to shared hosting or VPS somewhere.
Shared hosting
The good news is that shared hosting isn't very expensive. I've used Dreamhost for years for a number of sites and always been happy with them.
Read more about Dreamhosts options here. You should pick the Shared Hosting.
Domain name
As for the domain name, it's not really going to be visible to anyone (assuming you don't also put a marketing site there), so you can pick just about anything that makes sense. If your app is called ilanlist, and ilanlist.com is taken, just buy ilanlistbackend.com instead.
Web service
This is where things will hurt for you as I kind of sense you're not into making web thingies.

You might want to consider finding somebody who can make a simple web service for you, preferably in a very popular language such as php or ruby. This is important as the person who helps you will not be available forever, and when she's moved on to other things you need to be able to pick somebody from a large pool of people who knows the language. It's also somewhat important to pick a good framework, only web people who's in it for the love of pain code without frameworks nowadays. If you're going with php, I would consider
Laravel Lumen, and if ruby seems better, just go with
Ruby on Rails. There are more options out there, obviously. Regardless if you find somebody or decide to code the backend yourself (using a framework), you need to do the thinking of what's required. Not much difference from the thinking you use when coding B4X. "User needs to authenticate. And get a list of all lists stored on server. And download a list to mobile. And send a list back to mobile. And delete a list stored on server. Etc". A couple of good terms to read up on is
CRUD and
REST. Both those terms are discussed here in the forum also so you might get a head start using some code examples in here. This is a big field, but the good news is that you only need to grasp a very small part of it, thanks to the simplicity of your app.
Good luck, I hope this helps a little bit
